It is sure that if you are not doing link building of your website then it would be very hard to increase page rank of your website, mainly you have to do quality link building for increasing page rank of any website on the other hand it is good for optimizing keywords also.

If you do quality link building continuously then it would help you a lot in increasing page rank of your website, page rank is very important for any website.

Page rank is also connected to link building, higher the quality of your back links higher the page rank your site should have.

Yes,its true that more the number of quality backlinks, higher will be the page rank. you should get quality backlinks only. For this, you can do offpage optimization(article/blog/guest post submission,directory submission, reciprocal linking etc)